Math Flashcards

| 2x − 5 | = 19 Which of the following is the solution set for the equation above?

Answer: {−7, 12}

To solve an absolute value equation like |2x − 5| = 19, you must consider two cases. Case 1: 2x − 5 = 19. Adding 5 to both sides gives 2x = 24, so x = 12. Case 2: 2x − 5 = −19. Adding 5 to both sides gives 2x = −14, so x = −7. Therefore, the solution set for the equation is {−7, 12}.

If Maria left a $10.16 tip on a breakfast that cost $86.89, approximately what percentage was the tip?

Answer: 12%

To find the percentage of the tip, divide the tip amount by the original cost of the breakfast and then multiply by 100. So, ($10.16 ÷ $86.89) × 100. This calculation yields approximately 0.1169 × 100, which is 11.69%. When rounded to the nearest whole percentage, this is 12%. Therefore, the tip was approximately 12%.

A nurse working at a medical clinic earns $17.81 per hour. The nurse works three 8-hour shifts and one 12-hour shift every week, and is paid weekly. Weekly deductions are: federal tax $102.80, state tax $24.58, federal insurance $18.13, and family health insurance $52.15. What is the nurse's take-home pay each week?

Answer: $443.50

First, calculate the total hours worked per week: (3 shifts * 8 hours/shift) + 12 hours = 36 hours. Next, determine the gross weekly pay by multiplying the total hours by the hourly rate: 36 hours * $17.81/hour = $641.16. Then, sum all weekly deductions: $102.80 + $24.58 + $18.13 + $52.15 = $197.66. Finally, subtract the total deductions from the gross pay to find the take-home pay: $641.16 - $197.66 = $443.50.

How many imperial gallons are there in 1,400 liters?

Answer: 308

To convert liters to imperial gallons, you need to use the conversion factor that 1 imperial gallon is approximately equal to 4.54609 liters. Divide the total number of liters (1,400) by this conversion factor. So, 1400 liters / 4.54609 liters/gallon ≈ 307.97 gallons. Rounding this to the nearest whole number gives 308 imperial gallons.

Derek purchased concert tickets in the month of June for $73, $66, $96, $17, and $66 dollars. Which of the following is an accurate estimate of the total amount he spent on concert tickets in June?

Answer: $330

To estimate the total amount, round each concert ticket price to the nearest ten dollars. The prices become $70, $70, $100, $20, and $70. Summing these rounded values gives $70 + $70 + $100 + $20 + $70 = $330. This provides an accurate estimate of the total amount spent.

5y − 8 > 32

Answer: y > 8

To solve the inequality 5y - 8 > 32, first add 8 to both sides of the inequality: 5y > 32 + 8, which simplifies to 5y > 40. Next, divide both sides by 5 to isolate y. This results in y > 40 / 5, which simplifies to y > 8.

There are 48 students studying foreign language at the community college. If the only two foreign languages offered are French and Spanish, and 28 students are studying French, which of the following represents the ratio of students studying Spanish to the total number of foreign language students?

Answer: 5/12

First, determine the number of students studying Spanish by subtracting the number of French students from the total number of foreign language students: 48 - 28 = 20 students. The ratio of students studying Spanish to the total number of foreign language students is then 20/48. To simplify this ratio, divide both the numerator and the denominator by their greatest common divisor, which is 4. This yields a simplified ratio of 5/12.

What is 181.5% of 18?

Answer: 32.67

To calculate a percentage of a number, first convert the percentage to a decimal by dividing it by 100. So, 181.5% becomes 1.815. Then, multiply this decimal by the given number: 1.815 * 18. The result of this multiplication is 32.67.

Which of the following is equivalent to 0.0009?

Answer: 0.09%

To convert a decimal to a percentage, you multiply the decimal by 100. In this case, 0.0009 multiplied by 100 equals 0.09. Therefore, 0.0009 is equivalent to 0.09%.

The hourly rate for a male went up to $13.50 from $12.50. How much of a raise did he receive?

Answer: 8%

First, calculate the amount of the raise by subtracting the old hourly rate from the new one: $13.50 - $12.50 = $1.00. To find the percentage raise, divide the amount of the raise by the original hourly rate and multiply by 100. So, ($1.00 / $12.50) * 100 = 0.08 * 100 = 8%. The male received an 8% raise.

What is the cost of a DVD without the sales tax if you buy $22.90 for one that has a 7% sales tax included?

Answer: $21.40

Let 'x' be the original cost of the DVD without sales tax. With a 7% sales tax, the total cost is x + 0.07x, which simplifies to 1.07x. We are given that the total cost is $22.90, so 1.07x = $22.90. To find 'x', divide $22.90 by 1.07, which gives $21.4018... Rounding to two decimal places, the cost of the DVD without sales tax is $21.40.

A toll costs $2 for a vehicle and the driver, and an additional 75 cents for each passenger. How many people are in the automobile in total if the toll is $4.25?

Answer: 4

The toll for the vehicle and driver is $2.00. Subtract this from the total toll to find the cost attributed to passengers: $4.25 - $2.00 = $2.25. Since each additional passenger costs $0.75, divide the passenger cost by the per-passenger rate: $2.25 / $0.75 = 3 passengers. Finally, add the driver to the number of passengers to get the total number of people: 1 driver + 3 passengers = 4 people.

Leaving San Diego at 6:15 p.m. PST, a jet touched down in Philly at 2:45 a.m. EST. How much time was the flight?

Answer: 5 1/2 hours

The flight departs at 6:15 p.m. PST and arrives at 2:45 a.m. EST. Since EST is 3 hours ahead of PST, convert the departure time to EST: 6:15 p.m. PST + 3 hours = 9:15 p.m. EST. Now, calculate the duration from 9:15 p.m. EST to 2:45 a.m. EST. From 9:15 p.m. to midnight is 2 hours and 45 minutes, and from midnight to 2:45 a.m. is 2 hours and 45 minutes. Adding these together gives a total flight time of 5 hours and 30 minutes, or 5 1/2 hours.

Cost per square yard for carpet is $3. The carpeting-ready space measures 12 feet by 18 feet. What is the price of the carpet?

Answer: $72

First, calculate the area of the space in square feet: 12 feet * 18 feet = 216 square feet. Since the cost is per square yard, convert the area from square feet to square yards. Knowing that 1 yard = 3 feet, 1 square yard = 3 feet * 3 feet = 9 square feet. Divide the total square feet by 9 to get square yards: 216 sq ft / 9 sq ft/sq yd = 24 square yards. Finally, multiply the total square yards by the cost per square yard: 24 sq yd * $3/sq yd = $72.

A product's initial price is $125. What is the price of the goods if it is first discounted by 20% and then further discounted by 30%?

Answer: $70

First, apply the 20% discount to the initial price of $125: $125 * 0.20 = $25. The price after the first discount is $125 - $25 = $100. Next, apply the 30% discount to this new price of $100: $100 * 0.30 = $30. The final price after both discounts is $100 - $30 = $70.

Three baseball cards, three football cards, and six hockey cards make up a stack of sports cards. What is the likelihood that a hockey card will be chosen at random from a deck of cards?

Answer: 1/2

To find the likelihood of choosing a hockey card, first calculate the total number of cards: 3 baseball + 3 football + 6 hockey = 12 cards. The number of favorable outcomes (hockey cards) is 6. The probability is the number of favorable outcomes divided by the total number of outcomes, which is 6/12. This fraction simplifies to 1/2.

When x + y = z and x + y + 15 = 30, 40 - z =

Answer: 25

Given the equations x + y = z and x + y + 15 = 30, we can substitute 'z' for 'x + y' in the second equation. This yields z + 15 = 30. Solving for z, we subtract 15 from both sides: z = 30 - 15 = 15. Finally, substitute the value of z into the expression 40 - z: 40 - 15 = 25.

Of the following, which one is NOT a prime number?

Answer: 93

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Let's check the options: 127, 53, and 67 are all prime numbers. However, 93 is divisible by 3 (93 ÷ 3 = 31), meaning it has factors other than 1 and itself (namely 3 and 31). Therefore, 93 is not a prime number.

(x+3)(x+5) =

Answer: x²+8x+15

To expand the expression (x+3)(x+5), use the FOIL method (First, Outer, Inner, Last). Multiply the First terms (x*x = x²), the Outer terms (x*5 = 5x), the Inner terms (3*x = 3x), and the Last terms (3*5 = 15). Combine these results: x² + 5x + 3x + 15. Finally, combine the like terms (5x and 3x) to get x² + 8x + 15.

What does 4(x-y)+7 equal if x = y?

Answer: 7

Given that x = y, substitute x for y in the expression 4(x-y)+7. This changes the expression to 4(x-x)+7. Since x-x equals 0, the expression simplifies to 4(0)+7. Multiplying 4 by 0 gives 0, so the final result is 0+7, which equals 7.